Adaptive mach zehnder modulator linearization

ABSTRACT

The present invention is directed to optical communication systems and methods thereof. In various embodiments, the present invention provides method for linearizing Mach Zehnder modulators by digital pre-compensation and adjusting the gain of the driver and/or the modulation index. The pre-compensation can be implemented as a digital pre-compensation algorithm, which is a part of an adaptive feedback loop. There are other embodiments as well.

CROSS-REFERENCES TO RELATED APPLICATIONS

The present application is a continuation of and claims priority to U.S.application Ser. No. 15/223,724, filed Jul. 29, 2016, which is acontinuation of U.S. application Ser. No. 14/179,447 filed Feb. 12,2014, now U.S. Pat. No. 9,432,123, issued Aug. 30, 2016. This patentapplication is related to the U.S. patent application Ser. No.13/791,201, filed Mar. 8, 2013, now U.S. Pat. No. 9,020,346, issued Apr.28, 2015, which is incorporated by reference herein for all purposes.

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BACKGROUND OF THE INVENTION

The present invention is directed to optical communication systems andmethods thereof.

With advent of the Internet, cloud computing, and social networks, thereis an ever increasing demand on the data communication network. Toprovide high speed data communication, optical communication network isone of the top choices. To transmit data through optical communicationnetwork, electrical signals are modulated into optical signals.Electrical signals can be modulated in various ways, such as phasemodulation, amplitude modulation, polarization modulation, and/orcombination thereof.

For electro-optic modulation, Mach-Zehnder (MZ) modulators are oftenused. For example, in a MZ modulator, a beam splitter divides the laserlight into two paths, one of which has a phase modulator. The beams arethen recombined. Changing the electric field on the phase modulatingpath will then determine whether the two beams interfere constructivelyor destructively at the output, and thereby control the amplitude orintensity of the exiting light.

Over the past, there has been many implementation of MZ modulators, butunfortunately they have been inadequate as explained below. Therefore,improved system and methods for MZ modulation systems are desired.

BRIEF SUMMARY OF THE INVENTION

The present invention is directed to optical communication systems andmethods thereof. In various embodiments, the present invention providesmethod for linearizing Mach Zehnder modulators by digitalpre-compensation and adjusting the gain of the driver and/or themodulation index. The pre-compensation can be implemented as a digitalpre-compensation algorithm, which is a part of an adaptive feedbackloop. There are other embodiments as well.

According to an embodiment, the present invention provides a modulationsystem. The system has a nonlinear mapping module that is configured toperform a mapping process to generate a voltage signal using amodulation signal and a first modulation index. The system also includesa DAC module that is configured to convert the voltage signal to ananalog signal. The system additionally includes a driver module that isconfigured to generate a driving signal using the analog signal and again value. The driver module is configured to adjust the gain value inresponse to a compensation signal. The system also has a peak detectionmodule that is configured to determine a peak value associated with thedriving signal. The system additionally includes an MZ modulatorconfigured to generate an output signal using at least the drivingsignal. The output signal is associated a half wave voltage value.Moreover, the system includes a compensation module configured togenerate the compensation signal using at least the first modulationindex and the second module index. The second modulation index being afunction of the peak value and the half wave voltage value.

According to another embodiment, the present invention provides amodulation system that includes a nonlinear mapping module configured toperform a mapping process to generate a voltage signal using amodulation signal and a first modulation index. The system includes aDAC module configured to convert the voltage signal to an analog signal.Additionally, the system includes a driver module configured to generatea driving signal using the analog signal and a gain value. The drivermodule is further configured to adjust the gain value in response to acompensation signal. The system additionally includes a peak detectionmodule configured to determine a peak value associated with the drivingsignal. Furthermore, the system includes an MZ modulator configured togenerate an output signal using at least the driving signal. The outputsignal is associated a half wave voltage value. The system also includesa compensation module configured to generate the compensation signalusing at least the first modulation index and the second module index.The second modulation index is a function of the peak value and the halfwave voltage value.

According to another embodiment, the present invention provides a methodfor modulating signals. The method includes performing nonlinear mappinga modulation signal using a first modulation index to generate a voltagesignal. The method also includes processing the voltage signal using alinear equation. The method further includes converting the processedvoltage signal to an analog signal. The method additionally includesprocessing the analog signal at a gain value to generate a drivingsignal. Moreover, the method includes performing MZ modulation on thedriving signal to generate an output signal. The method also includesdetermining a second modulation index based at least on the drivingsignal and the first modulation index. The method further includesadjusting the gain value using the second modulation index.

It is to be appreciated that embodiments of the present inventionprovides numerous advantages over conventional systems and methods. Asdescribed below in further details, the linearization provided by theembodiments of the present invention improves performance of MZmodulators, and thus enhancing optical network and other applications.In addition, various aspects of the present invention are compatiblewith existing techniques, and can be readily incorporated or otherwiseadopted into existing systems. There are other benefits as well.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified diagram illustrating a coherent optical system.

FIG. 2 is a simplified diagram illustrating a transmitter for coherentoptical system.

FIG. 3 is a simplified graph illustrating the total harmonic distortionand loss of a MZ modulator.

FIG. 4 is a simplified diagram illustrating pre-distortion functioningassociated with linearizing a MZ modulator.

FIG. 5 is a simplified graph illustrating a nonlinear pre-distortion mapfor compensating MZ nonlinearity.

FIG. 6 is a simplified block diagram illustrating a digitalimplementation of pre-distortion portion of a MZ modulator.

FIG. 7 is a simplified graph illustrating effect of gain mismatch ontotal harmonic distortion.

FIG. 8 is a simplified graph illustrating ratio of powers in harmonicsas a function of modulating index.

FIG. 9 is a graph illustrating frequency dependency of a MZ voltage.

FIG. 10 is a simplified block diagram illustrating a feedback look forsetting driver gain for MZ linearization.

FIG. 11 is a simplified block diagram illustrating a feedback look forsetting nonlinear pre-distortion of MZ linearization.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is directed to optical communication systems andmethods thereof. In various embodiments, the present invention providesmethod for linearizing Mach Zehnder modulators by digitalpre-compensation and adjusting the gain of the driver and/or themodulation index. The pre-compensation can be implemented as a digitalpre-compensation algorithm, which is a part of an adaptive feedbackloop. There are other embodiments as well.

The following description is presented to enable one of ordinary skillin the art to make and use the invention and to incorporate it in thecontext of particular applications. Various modifications, as well as avariety of uses in different applications will be readily apparent tothose skilled in the art, and the general principles defined herein maybe applied to a wide range of embodiments. Thus, the present inventionis not intended to be limited to the embodiments presented, but is to beaccorded the widest scope consistent with the principles and novelfeatures disclosed herein.

In the following detailed description, numerous specific details are setforth in order to provide a more thorough understanding of the presentinvention. However, it will be apparent to one skilled in the art thatthe present invention may be practiced without necessarily being limitedto these specific details. In other instances, well-known structures anddevices are shown in block diagram form, rather than in detail, in orderto avoid obscuring the present invention.

The reader's attention is directed to all papers and documents which arefiled concurrently with this specification and which are open to publicinspection with this specification, and the contents of all such papersand documents are incorporated herein by reference. All the featuresdisclosed in this specification, (including any accompanying claims,abstract, and drawings) may be replaced by alternative features servingthe same, equivalent or similar purpose, unless expressly statedotherwise. Thus, unless expressly stated otherwise, each featuredisclosed is one example only of a generic series of equivalent orsimilar features.

Furthermore, any element in a claim that does not explicitly state“means for” performing a specified function, or “step for” performing aspecific function, is not to be interpreted as a “means” or “step”clause as specified in 35 U.S.C. Section 112, Paragraph 6. Inparticular, the use of “step of” or “act of” in the Claims herein is notintended to invoke the provisions of 35 U.S.C. 112, Paragraph 6.

Please note, if used, the labels left, right, front, back, top, bottom,forward, reverse, clockwise and counter clockwise have been used forconvenience purposes only and are not intended to imply any particularfixed direction. Instead, they are used to reflect relative locationsand/or directions between various portions of an object.

As explained above, optical communication networks are widely used fordata communication. In order to meet increasing demands of data traffic,optical communication systems are transitioning from non-coherentarchitecture to coherent architecture. FIG. 1 is a simplified diagramillustrating a coherent optical system.

Among other features, coherent optical communication network systems, incomparison to non-coherent systems, have better sensitivity and higherspectral efficiency, thereby being capable of tolerating higherchromatic and polarization mode dispersion. In addition, coherentreceivers allow for phase and amplitude modulation. For example,modulation formats such as QAM and OFDM modulation have been consideredfor coherent optical systems. Techniques such as pulse shaping andpre-compensation for chromatic dispersion can be deployed at thetransmitters of coherent systems. To implement coherent systems, lineartransmitter is needed.

For modulation, MZ modulators are used to modulate the magnitude andphase of the electric field at the transmitter, shown in FIG. 2. FIG. 2is a simplified diagram illustrating a transmitter for coherent opticalsystem. Here u(t) is the modulating signal, which is amplified by alinear amplifier or driver to produce the signal x(t). We will assumethat u(t) is normalized such that −1<=u(t)<=1. Ei and Eo are the inputand output optical fields of the MZ modulator.

The transfer function of an ideal lossless MZ biased at the null pointis given by

$\begin{matrix}{E_{o} = {E_{i}{\sin \left( {\frac{\pi}{2\; V_{\pi}}{x(t)}} \right)}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

V_(π) is the half wave voltage of the MZ modulator. Since coherentreceivers detect the electric field (and not optical power), therelevant transfer function for the MZ modulator is from the electricalRF port to the optical electric field. As can be seen from the aboveequation, the transfer function is not linear, and it is needed tolinearize the transmitter.

One method of linearizing the modulator is to make the modulating signalsufficiently small so that the approximation below holds:

$\begin{matrix}{E_{o} \approx {E_{i}\frac{\pi}{2\; V_{\pi}}{x(t)}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

Unfortunately, making the modulating signal sufficiently small leads toa loss of power at the output of the modulator. As a result of the smallmodulating signal, additional optical amplification is needed. If x(t)is increased, the nonlinearity of the modulator increases. For example,one measure of the nonlinearity is the total harmonic distortion (THD)which is a measure of the distortion when x(t) is a sinusoidal signal,x(t)=A sin(ω t). FIG. 3 is a simplified graph illustrating the totalharmonic distortion and loss of a MZ modulator. More specifically, FIG.3 shows an increase in THD when the amplitude of the modulating signalis increased. Also shown in FIG. 3 is the corresponding loss in theoutput optical power of the modulator as the input amplitude isdecreased.

An alternate method is to remap the signal using the inversetransformation of the MZ modulator, as shown in FIG. 4. FIG. 4 is asimplified diagram illustrating pre-distortion associated withlinearizing a MZ modulator. Let the gain of the driver be such that:

−αV _(π) <x(t)<αV _(π) where 0<α<1   Equation 3:

The variable α here is referred to as the modulation index. Let the mapfrom u(t) to v(t) be defined by

$\begin{matrix}{{v(t)} = {{\frac{1}{\alpha}{\sin^{- 1}\left( {\beta \; {u(t)}} \right)}\mspace{14mu} {where}\mspace{14mu} \beta} = {\sin \left( {\alpha \frac{\pi}{2}} \right)}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

Since we have assumed that u(t) is normalized to −1<=u(t)<=1, βu(t) alsolies in the range [−1, 1] and the map from u(t) to v(t) is well defined.Further −π/2<v(t)<π/2.

In order to satisfy the condition in equation 3, the gain of the driveris given by the equation

$\begin{matrix}{G = \frac{2\alpha \; V_{\pi}}{\pi}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

Then the output electric field of the MZ modulator is:

$\begin{matrix}\begin{matrix}{E_{o} = {E_{i}{\sin \left( {\frac{\pi}{2\; V_{\pi}}{x(t)}} \right)}}} \\{= {E_{i}{\sin \left( {\frac{\pi}{2\; V_{\pi}}{{Gv}(t)}} \right)}}} \\{= {E_{i}{\sin \left( {\frac{\pi}{2\; V_{\pi}}\frac{2\alpha \; V_{\pi}}{\pi}\frac{1}{\alpha}{\sin^{- 1}\left( {\beta \; u} \right)}} \right)}}} \\{= {E_{i}\beta \; u}}\end{matrix} & {{Equation}\mspace{14mu} 6}\end{matrix}$

The output E-field is a linear function of the signal u(t) and β is theeffective gain of this linearized transmitter. Note that the mapping inEquation 4 is a function of the modulation index α. Further, the gain ofthe driver is also a function of the modulator half wave voltage V_(π)and the modulation index α.

FIG. 5 is a simplified graph illustrating a nonlinear pre-distortion mapfor compensating MZ nonlinearity. More specifically, FIG. 5 shows themap from u→v for different values of the modulation index α. As α→0, thetransformation becomes linear which is to be expected because for smallswings relative to V_(π), sin(π/(2V_(π))X)→π/(2V_(π))X. In this case theMZ behaves like a linear element and no pre-compensation is required.

As an example, the map from u→v can be implemented digitally, as shownin FIG. 6. FIG. 6 is a simplified block diagram illustrating a digitalimplementation of pre-distortion portion of a MZ modulator.

If V_(π) of the modulator is known and the gain of the driver can befixed accurately, then the system can be set up for a given value of α,which is used in the DSP for the pre-compensation algorithm. However dueto variations in V_(π) and in the gain of the driver, the modulationindex can vary.

Next consider the case when the signal is pre-compensated for a swing ofα, but the gain of the driver is set such that the actual modulationindex is α′. This is effectively a mismatch between the gain of thedriver and the value of the modulation index assumed in the DSP. FIG. 7is a simplified graph illustrating effect of gain mismatch on totalharmonic distortion. More specifically, FIG. 7 shows the effect of thisgain mismatch on the linearity of the transmitter for different drivestrengths. As shown, the mismatch has a greater effect for larger drivestrengths.

Therefore, it is to be appreciated that according to various embodimentsof the present invention, an adaptive linearization mechanism isprovided for coherent optical communication systems, and a feedback loopis used to adjust gain and/or pre-distortion at the input of the MZmodulator.

To measure the modulated signal (e.g., for the purpose of measuring MZmodulator distortion) at the output of the Mach Zehnder, a high speedreceiver is needed. High-speed receivers are typically expensive toimplement. As explained above, the modulation index is required tolinearize the modulator and it can be determined without directlymeasuring the modulated optical signal. This feature allows forlinearization of the Mach Zehnder modulator. In various embodiments, alow frequency transmit and receive path is provided at the transmitter,which can be implemented via the DC bias port of the MZ and a low speedphoto diode (e.g., integrated into the MZ modulator) that are used toset the bias point of the MZ. A biasing technique is used to modulatethe bias port with a low frequency sinusoidal signal of low amplitude.To set the MZ at the null bias point, the DC bias is varied until thefundamental and odd harmonics of the modulating signal are minimized(e.g., even harmonics are maximized).

In various embodiments, the ratio of the DC to the 2^(nd) harmonic orthe ratio of the second harmonic to the fourth harmonic is measured.These ratios allow for measurement of the modulation index. The use ofthese ratios can be demonstrated by using Equation 1: by letting themodulating signal x(t) be a sinusoidal signal of the form x(t)=A sin(ω₀t). The output power is obtained by squaring Equation 1, as shown inEquation 7 below:

$\begin{matrix}{P_{o} = {\frac{P_{i}}{2}\left( {1 - {\cos \left( {\frac{2\pi}{2\; V_{\pi}}A\; {\sin \left( {\omega_{0}t} \right)}} \right)}} \right)}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

By using standard Fourier series analysis, Equation 8 below is obtained:

$\begin{matrix}{{\cos \left( {\beta \; {\sin (\theta)}} \right)} = {{J_{0}(\beta)} + {\sum\limits_{k = 1}^{\infty}\; {2\; {J_{2\; k}(\beta)}{\cos \left( {2\; k\; \theta} \right)}}}}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

In Equation 8, J_(n)( ) is the nth order Bessel function of the firstkind. Using Equation 7 and Equation 8, Equation 9 below can be obtained,which describes the output power for a sinusoidally modulated MZ biasedat the null point:

$\begin{matrix}{{P_{o} = {\frac{P_{i}}{2} + {\frac{P_{i}}{2}\left( {{J_{0}\left( {2\; X} \right)} + {2\; {J_{2}\left( {2\; X} \right)}{\cos \left( {2\omega_{0}t} \right)}} + {2\; {J_{4}\left( {2\; X} \right)}{\cos \left( {4\omega_{0}t} \right)}} - \ldots}\mspace{14mu} \right)}}},} & {{Equation}\mspace{14mu} 9}\end{matrix}$

Where:

${X = \frac{\pi \; A}{2\; V_{\pi}}},\mspace{50mu} {A = {{amplitude}\mspace{14mu} {of}\mspace{14mu} {sinusoid}}},$

From Equation 9, Equation 10 and Equation 11 can be determined:

$\begin{matrix}{\frac{{Power}\mspace{14mu} {in}\mspace{14mu} {DC}}{{Power}\mspace{14mu} {in}\mspace{14mu} 2\; {nd}\mspace{14mu} {harmonic}} = \frac{1 + {J_{0}\left( {2\; X} \right)}}{2\; {J_{2}\left( {2\; X} \right)}}} & {{Equation}\mspace{14mu} 10} \\{\frac{{Power}\mspace{14mu} {in}\mspace{14mu} 2\; {nd}\mspace{14mu} {harmonic}}{{Power}\mspace{14mu} {in}\mspace{14mu} 4\; {th}\mspace{14mu} {harmonic}} = \frac{J_{2}\left( {2\; X} \right)}{J_{4}\left( {2\; X} \right)}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

FIG. 8 is a simplified graph illustrating ratio of powers in harmonicsas a function of modulating index. More specifically, ratios P₀/P₂ andP₂/P₄ are shown in FIG. 8. For example, by measuring either of theseratios, the value of X in Equation 9 can be determined. For a knownvalue of “A” (i.e., amplitude of sinusoid), the value of V_(π) can bedetermined. Depending on the implementation, the power in the harmonics,P₀, P₂, and P₄ can be measured by analog means using analog filters andpower detectors, or by using an ADC and processing the samplesdigitally.

Once the value of V_(π) is determined, it can be compared to theamplitude of the modulating signal x(t) in order to determine themodulation index. At the RF port of the MZ modulator, the maximum valueof the drive signal can be determined with a peak detector. The ratio ofthe peak detector output to V_(π) now gives the actual modulation indexof the system. The gain of the driver can be adjusted till the requiredratio is obtained.

As an example, assume that MZ is to be driven at 80% of V_(π), i.e. thepeak value of x(t) should be 0.8*V_(π). Hence the digitalpre-compensation for the MZ sinusoidal nonlinearity is computed for avalue of α=0.8. Assume that a measurement on the photodiode output ofthe MZ modulator shows that the ratio of the powers in the 2^(nd) to the4^(th) harmonic is 10*log 10(P₂/P₄)=35 dB. As can be seen from FIG. 8,X=0.06 corresponds to this ratio of P₂/P₄. Assume that a separatemeasurement of A, the amplitude of the sinusoidal modulating signalgives A=0.2V. Then V_(π)=π*0.2/(2*0.06)=5.24V. Next assume that the peakdetector at the output of the driver gives a value of 5V. The drivergain is now adjusted till the peak detector output corresponds to amaximum drive voltage of 0.8*5.24=4.2V. At this point the MZ is beingdriven at the required value and the digital pre-compensation matchesthe analog drive signal. It is to be appreciated this process isimplemented as a MZ controller algorithm according to variousembodiments of the present invention.

According to the process described above, the measured value of V_(π) isat a low frequency. V_(π) is a function of frequency, and the dependenceis mainly due to the high frequency loss in the electrical componentsand the electrical waveguides in the MZ modulator. FIG. 9 is a graphillustrating frequency dependency of a MZ voltage.

The frequency dependence of V_(π) can be expressed as

V _(π) =V _(π0) H(f)   Equation 12:

where V_(π) is the DC (low frequency) value of V_(π) and H(f) representsthe frequency dependence. We assume that the inverse of this transferfunction is well defined and is denoted as U(f), i.e.,

U(f)=1/H(f)   Equation 13:

The output of the modulator can then be expressed as

$\begin{matrix}{E_{o} = {E_{i}{\sin \left( {\frac{\pi}{2\; V_{\pi \; 0}}{^{- 1}\left( {{U(f)}{X(f)}} \right)}} \right)}}} & {{Equation}\mspace{14mu} 14}\end{matrix}$

where

is the inverse Fourier transform and X(f) is the Fourier transform ofx(t). Hence we can equalize the signal after the nonlinear map with thetransfer function H_(eq)(f)=1/U(f) to get rid of this frequencydependency and effectively keep V_(π) constant across frequency.

$\begin{matrix}\begin{matrix}{E_{o} = {E_{i}{\sin \left( {\frac{\pi}{2\; V_{\pi \; 0}}{^{- 1}\left( {{U(f)}{X(f)}{H_{eq}(f)}} \right)}} \right)}}} \\{= {E_{i}{\sin \left( {\frac{\pi}{2\; V_{\pi 0}}{^{- 1}\left( {X(f)} \right)}} \right)}}} \\{= {E_{i}{\sin \left( {\frac{\pi}{2\; V_{\pi 0}}{x(t)}} \right)}}}\end{matrix} & {{Equation}\mspace{14mu} 15}\end{matrix}$

This now reduces to the previous case where V_(π) was assumed to beconstant (see Equation 1), and the techniques previously described areapplicable. Once again the map from the signal u(t) to the outputelectric field of the MZ modulator is a linear mapping.

The resulting system is shown in FIG. 10. For example, FIG. 10 is asimplified block diagram illustrating a feedback look for setting drivergain for MZ linearization according to an embodiment of the presentinvention. This diagram is merely an example, which should not undulylimit the scope of the claims. One of ordinary skill in the art wouldrecognize many variations, alternatives, and modifications. For example,the process performed is effectively a linear system from u(k) to E_(o).

Another way to provide MZ linearization is to modify the nonlinear mapbased upon the measured value α′ and leave the gain of the driver fixed.FIG. 11 is a simplified block diagram illustrating a feedback look forsetting nonlinear pre-distortion of MZ linearization according to anembodiment of the present invention. This diagram is merely an example,which should not unduly limit the scope of the claims. One of ordinaryskill in the art would recognize many variations, alternatives, andmodifications. To use the numerical example worked previously, thedigital pre-compensation is initially calculated for a value of α=0.8,the measured value of V_(π)=5.24 V and a peak detector value of 5V givesα′=5/5.24=0.95. This value is fed back to the nonlinear map in the DSPand the pre-compensation is recomputed for this new value of α′=0.95.The gain of the driver is left unchanged. The pre-compensation nowmatches the analog drive signal.

While the above is a full description of the specific embodiments,various modifications, alternative constructions and equivalents may beused. Therefore, the above description and illustrations should not betaken as limiting the scope of the present invention which is defined bythe appended claims.

What is claimed is:
 1. A method of transferring data using acommunication system, the communication system comprising: a transmitterdevice comprising: a nonlinear mapping module being configured toperform a mapping process to generate a voltage signal using amodulation signal and a first modulation index using an inversetransformation function; a DAC module being configured to convert thevoltage signal to an analog signal; a driver module being configured togenerate a driving signal using the analog signal and a gain value, thedriver module further being configured to adjust the gain value inresponse to a compensation signal; an MZ modulator being configured togenerate an output signal using at least the driving signal, the outputsignal being associated a half wave voltage value; and an adaptivefeedback loop being configured to generate the compensation signal basedon a peak value associated with the driving signal and a ratio between aDC power and a second order harmonic values of measured output power;using the communication to transfer data.
 2. The system of claim 1wherein the second modulation index is determined by computing a ratiobetween the peak value and the half wave voltage value.
 3. The system ofclaim 1 further comprising a linear equation module for processing thevoltage signal.
 4. The system of claim 1 wherein the adaptive feedbackloop comprises a peak detection module being configured to determine thepeak value.
 5. The system of claim 1 wherein the MZ modulator iselectrically coupled to a photo diode.
 6. A method of transferring datausing an optical communication network, the network comprising atransmitter device comprising: a nonlinear mapping module beingconfigured to perform a mapping process to generate a voltage signalusing a modulation signal and an adjustable modulation index value usingan inverse transformation function; a DAC module being configured toconvert the voltage signal to an analog signal; a driver module beingconfigured to generate a driving signal using the analog signal and again value; an MZ modulator being configured to generate an outputsignal using at least the driving signal, the output signal beingassociated a half wave voltage value; and an adaptive feedback loopbeing configured to generate to determine the adjustable modulationindex value based on the peak value associated with the driving signaland a ratio between a second order harmonic and a fourth order harmonicvalues of measured output power; and transferring data using the opticalcommunication system.
 7. The system of claim 6 further comprising alinear equation module for processing the voltage signal, the linearequation module being configured to provide a signal compensation basedat least on the modulation index value.
 8. The system of claim 6 whereinthe MZ modulator comprises a photo diode.
 9. The system of claim 6wherein the half wave voltage value is determined based on the amplitudevalue and measured harmonics of the output signal.
 10. A method formodulating signals for an communication system, the method comprising:performing nonlinear mapping a modulation signal using a firstmodulation index to generate a voltage signal using an inversetransformation function and an adjustable modulation index value;processing the voltage signal using a linear equation; converting theprocessed voltage signal to an analog signal; generating a drivingsignal based on the analog signal; measuring a peak voltage of thedriving signal in a transmitter; performing MZ modulation on the drivingsignal to generate an output signal; determining a ratio between a DCpower and a second order harmonic values of measured output power;determining a second modulation index based at least on the drivingsignal and the first modulation index; modifying the adjustablemodulation index value using the second modulation index and the ratio;and transferring data.
 11. The method of claim 10 further comprisinggenerating an optical output signal.
 12. The method of claim 10 furthercomprising measuring one or more harmonics of the output signal.
 13. Themethod of claim 10 further comprising measuring an amplitude and one ormore harmonics associated with the output signal.
 14. The method ofclaim 10 further wherein the driving signal is characterized by asubstantially constant gain.
 15. The method of claim 10 furthercomprising determining a ratio between the peak value and a half wavevoltage value.
 16. The method of claim 10 further comprising amplifyingthe analog signal.
 17. The method of claim 10 further comprisingmeasuring a bias amplitude associated with an MZ modulator.